A spatially aggregating population model involving size-distributed dynamics

Many biological populations tend to aggregate in response to concentration gradients of a chemoattractant secreted by themselves. The present study is motivated by the aggregation observed in Blattella germanica. At properly high densities, B. germanica individuals grow faster than do isolated ones, and they aggregate so as to maintain such densities (Ishii [1969]). This prominent feature suggests that there is evidently a correlation between the growth rate and population density of individuals.